Passive sampling device and method of sampling and analysis

ABSTRACT

The invention provides a device and method to quantitatively measure concentrations of volatile organic compound vapors below the ground surface using a preferably “fully” passive device that is placed in a drilled or bored hole for a specified period of time, wherein the sampler constrains the uptake rate to match values that minimize or eliminate the starvation effect and provide acceptable sensitivity for most soil types as calculated via mathematical models.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of and claims priority to U.S. patentapplication Ser. No. 14/022,960, filed Sep. 10, 2013, entitled PassiveSampling Device and Method of Sampling and Analysis, and claims thebenefit of U.S. Provisional Patent Application No. 61/700,667, filedSep. 13, 2012, entitled Low-Uptake Waterloo Membrane Sampler forQuantitative Passive Soil Vapor Concentration Measurement.

BACKGROUND OF THE INVENTION

Several different types of passive samplers are known in the art formeasuring relative abundance of volatile organic compound (VOC) vaporsbelow the ground surface, but the uptake rate of the sampler and thedelivery rate of vapors to the void space in which the sampler isdeployed has not been known or controlled, so the ability to quantifyvapor concentrations from the mass of compounds sorbed was not veryaccurate or precise. As a result, they have been labeled as useful onlyfor screening purposes and not for purposes requiring higher levels ofdata validation such as human health risk assessment.

Prior passive soil vapor sampling devices include the Gore® Sorber orGore® Module, Petrex Tubes, Beacon's B-Sure Test Kit, and EMFLUXcartridges. Each of these consists of sorbent media exposed to a voidspace in the subsurface with no rigorous attempt to maintain an uptakerate by the sampler that is lower than the delivery rate of vapors fromthe soil. In this case, the uptake rate varies according to the porosityand moisture content of the soil, which is seldom consistent.

For some existing passive soil vapor samplers, concentrations can atbest be estimated by deriving an empirical relationship between the masssorbed and concentrations measured with conventional active soil gassampling methods; however, this has limitations because the empiricalrelationship depends on site-specific conditions, which may varyunpredictably between sites and sampling locations. Others (e.g., theGore™ Module) have attempted to use an equation to calculate the uptakerate from the soil moisture and porosity, but they did not derive theirequations from first principles, and have not shown their approachprovides accurate and precise concentration data.

What is needed is a sampler that constrains the uptake rate of thesampler to be lower than the delivery rate for most commonly encounteredconditions of soil porosity and moisture content, to provide consistentquantification of soil vapor concentrations. The uptake rate must alsobe high enough to allow the sampler to detect low soil vaporconcentrations with a practical sampling duration.

SUMMARY OF THE INVENTION

The invention provides a method to quantitatively measure concentrationsof VOC vapors below the ground surface using a preferably “fully”passive (i.e., relies on diffusion and permeation only with no power,pumping or forced advection) device that is placed in a drilled or boredhole for a specified period of time, which is supported by mathematicalmodels and controlled field experiments. For short sample periods, thereis an option to purge stagnant soil gas from the void-space in which thesampler is deployed; therefore, the invention includes both fullypassive methods as well as methods where forced advection isincorporated briefly at the outset of the sampling period.

In an illustrative embodiment of the invention, the sampler comprises acontainer filled with a sorbent medium and having an opening which maybe covered with a membrane. The membrane preferably has a uniformthickness. The sorbent medium is suitable to retain and recover thetarget analytes using solvent extraction or thermal desorption. Thesampler constrains the uptake rate to values that minimize or eliminatethe starvation effect for most soil types as calculated via mathematicalmodels. In exemplary embodiments of the invention, adequate sensitivityis provided (ability to detect low concentrations) with practical sampledurations.

Two mathematical models (transient and steady-state) were used tocalculate the relationship between the delivery rate of vapors to thevoid space in which a passive sampler is deployed and the soil moistureand porosity. The uptake rate of the sampler is similar to or smallerthan the delivery rate of vapors from the surrounding soil for mostcommonly-encountered soil moisture contents, so the concentration ofvapors in the void space within which the sampler is exposed is similarto the concentration in the surrounding soil gas throughout the majorityof the sampling interval.

VOC vapor concentrations below the ground surface are measured using theinventive passive sampler to sorb (or trap) VOC vapors at known uptakerates, which allows the concentration to be calculated from the mass ofeach compound sorbed and the exposure time of the sample (both of whichcan be measured with acceptable accuracy using existing methods).

During the exposure time (also known as the sampling period, the sampleduration or combinations of these terms), vapors dissolve into themembrane in the sampler and permeate across it at rates that aredistinct for each chemical. The uptake rates are also proportional tothe linear temperature programmed retention indices (LTPRI) of thecompounds or chemicals of interest for analysis by gas chromatographywhere the stationary phase is the same material as used for the membrane(e.g., polydimethyl siloxane, or PDMS). The membrane area, i.e. theopening area, and the membrane thickness may be selected to optimize theuptake rate for the specific compounds or chemicals of interest.

The invention further includes a method of sampling that comprisesemploying a plug to seal the drillhole or borehole slightly above apassive sampler. In an illustrative embodiment of the method, a plasticsleeve is cut to a length of about 30 cm longer than the depth from theground surface to the location where the seal is desired. A foam plug(slightly larger in diameter than the borehole) is compressed and placedinside one end of a thin walled rigid pipe. A dowel is placed inside thepipe and the pipe is positioned inside the plastic sleeve. A borehole isdrilled and the soil removed. The passive sampler is then lowered to thetarget depth using an inert tether. The plastic sleeve, pipe and dowelare then lowered to a depth slightly above the sampler. The foam is thenforced out of the pipe using the dowel. The foam expands and pressesagainst the borehole wall and form a seal just above the passive samplerduring the sampling period.

The invention includes determination of the optimal uptake rates, thesamplers for quantitative passive soil vapor concentration measurementand the methods of sampler deployment, sealing, retrieval and analysisto quantitatively measure concentrations of VOC vapors below the groundsurface according to any of the embodiments described herein.

DESCRIPTION OF THE DRAWINGS

Illustrative embodiments of the invention are best understood from thefollowing detailed description when read with the accompanying drawings.

FIG. 1 shows the effective diffusion coefficient versus water-filledporosity for TCE in a soil with 37.5% total porosity, typical of a sandysoil.

FIG. 2 is a schematic of the transient mathematical model domainincluding boundary and initial conditions according to an illustrativeembodiment of the invention.

FIG. 3 shows the simulated mass of TCE delivered by diffusion fromsurrounding soil to the void space versus time for range of water-filledporosities in a 10 cm tall and 2.5 cm diameter void-space in a sandysoil with 37.5% total porosity and an initial soil vapor concentrationof 100 μg/m³, assuming no removal of mass by a passive sampler.

FIG. 4 shows the diffusive delivery rate of TCE versus time for a rangeof water-filled porosities for mass entering void space of a 10 cm talland 2.5 cm diameter void-space in a soil with 37.5% total porosity andan initial soil vapor concentration of 100 μg/m³, assuming no removal ofmass by a passive sampler.

FIG. 5 shows the relationship between the instantaneous diffusivedelivery rate of TCE vapors into the void space versus the percent ofmass entering the void space for different water-filled porosities,where Mass_(max), is the maximum vapor mass in the void space atequilibrium, assuming a 2.5 cm diameter borehole in a soil with 37.5%total porosity, initial soil vapor concentration of 100 μg/m³ and noremoval of mass by a passive sampler.

FIG. 6 shows the superimposed diffusive delivery rate of TCE plus uptakerate versus time for a 10 cm tall and 2.5 cm diameter void space in asoil with 37.5% total porosity containing a passive sampler with anuptake rate of 1 mL/min at various levels of water-filled porosity.

FIG. 7 depicts the diffusive delivery rate calculated using thesteady-state model corresponding to various 8 values as a function ofwater-filled porosity for a 10 cm tall and 2.5 cm diameter void-spaceassuming r₃=1 m.

FIG. 8 shows the diffusive delivery rate calculated using thesteady-state model corresponding to various r₃ values as a function ofwater-filled porosity for a 10 cm tall and 2.5 cm diameter void-spaceassuming δ=0.75.

FIG. 9 depicts a disposable passive sampler, according to anillustrative embodiment of the invention.

FIG. 10 depicts a reusable passive sampler, according to an illustrativeembodiment of the invention.

FIG. 11 is a schematic diagram of a first option for semi-permanentprobes for passive soil vapor sampling, according to an illustrativeembodiment of the invention.

FIG. 12 is a second option for semi-permanent probes for passive soilvapor sampling, according to an illustrative embodiment of theinvention.

FIGS. 13a-c depict a method of sampling in a temporary (uncased) hole,according to an illustrative embodiment of the invention.

FIGS. 14a,b shows the relative concentration (passive/active, or C/Co)for 1,1-DCE and TCE, respectively, at a field sampling demonstrationsite with soil gas probes constructed as shown in FIG. 11, including forcomparison purposes data from other passive sampling devices.

FIGS. 15a,b show the correlation between passive samples and Summa®canister samples at a field sampling demonstration site with soil gasprobes constructed as shown in FIG. 12 (for FIG. 15a ) or sub-slabprobes (for FIG. 15b ), with linear regressions and correlationcoefficients (R²), including for comparison purposes data from otherpassive sampling devices.

FIG. 16 shows the relative concentration (passive/Summa®) of fourdifferent VOCs as a range of different sampling periods for a sampler ina 1-inch (2.54 cm) diameter temporary probe as shown in FIG. 13a -c.

FIGS. 17a,b show the relative concentration (C_(passive)/C_(active))versus (FIG. 17a ) uptake rate (UR), and (FIG. 17b ) (UR×sampletime)/Void Volume.

DETAILED DESCRIPTION OF THE INVENTION

The invention provides a method to quantitatively measure concentrationsof VOC vapors below the ground surface using a preferably “fully”passive (i.e., relies on diffusion and permeation only) device that isplaced in a drilled or bored hole for a specified period of time,supported by mathematical models and controlled field experiments. Thedevice sorbs or traps VOC vapors at known uptake rates, which allow theconcentration to be calculated from the mass of each compound sorbed(quantified by a chemical analysis laboratory) and the exposure time.

The process improvement consists of: calculations using two mathematicalmodels (transient and steady-state) to derive the relationship betweenthe delivery rate of vapors to the void space in which a passive sampleris deployed and the soil moisture and porosity; a new sampling devicethat constrains the uptake rate to a desired value, which is preferablylower than typical rates of vapor delivery to the void space viadiffusion through the surrounding soil but high enough to provideacceptable sensitivity within a reasonable period of sampling, and;methods of sampler deployment, sealing, retrieval and analysis. If theuptake rate of the sampler is similar to or smaller than the deliveryrate of vapors from the surrounding soil, the concentration of vapors inthe void space within which the sampler is exposed will be similar tothe concentration in the surrounding soil gas throughout the majority ofthe sampling interval. Past attempts at quantitative passive soil vaporsampling did not control the uptake rate at levels below the rate ofvapor diffusion toward the sampler from the surrounding soil andtherefore, likely suffered from the “starvation effect”, where theconcentrations of VOC vapors in the void space are lower thanconcentrations in the surrounding soil, resulting in a negative bias inthe concentration measurements, or an inconsistent correlation betweenthe mass sorbed per unit time and the concentration (i.e., unknown orunpredictable uptake rate). The mathematical models will now bedescribed according to an illustrative embodiment of the invention.

Transient and steady-state mathematical models of radial vapor diffusionto a drilled hole were developed to help understand vapor transportrates during passive diffusive soil vapor sampling. These simulationsprovide a technical basis for the design of passive samplers in order toachieve reliable quantitative soil vapor concentrations. The sampler isdesigned to, and will have a known or predictable uptake rate throughoutthe sample duration for most commonly-encountered soil moisture andporosity conditions.

Quantitative passive samplers are of two general varieties: 1)equilibrium samplers (where the concentration in the samplerequilibrates with the surrounding medium, including a partitioningcoefficient if the sampler is composed of a different medium), and 2)kinetic samplers (where the sampler is designed to have a constantuptake rate throughout the sample duration). The illustrative modeldeals with kinetic passive samplers.

The basic principles of operation for quantitative passive samplers areas follows. Each device is supplied by the laboratory certified cleanand sealed in air-tight packing. The sampler is exposed to the air, gasor atmosphere being investigated for a measured amount of time (t),during which VOCs diffuse or permeate into the device from thesurrounding gas or atmosphere in response to the chemical potential(i.e., concentration) gradient. A certain mass (M) of VOCs is sorbed (ortrapped) by the sorptive medium within the device. After sampling, themass sorbed is quantified. The time-weighted average (TWA) concentration(C) of a particular analyte in the medium being sampled is thencalculated as follows:

$\begin{matrix}{C = \frac{M}{{UR} \times t}} & (1)\end{matrix}$

where:

C=TWA concentration in the sampled air [μg/m³]

M=mass of analyte on the sorbent, blank-corrected if needed [pg]

UR=passive sampler uptake rate [mL/minute]

t=sampling time or exposure duration [minutes]

(note that there are two offsetting conversion factors from pg to μg andmL to m³)

The UR has units of vol/time, but it is important to recognize that itdoes not represent a flow rate (sampling occurs by diffusion andpermeation only, with no net flow of gas); rather, it is simply a numberequivalent to the flow rate that would produce the same mass loading onan active sampler that had air pulled through it for the same C and t.The mass sorbed and exposure duration are both measured by conventionalmethods with acceptable accuracy, so the uptake rate is a key factorcontrolling the accuracy of the calculated concentration. Quantitativepassive samplers are designed to control the uptake rate of chemicalsusing a fixed cross-sectional opening area and diffusion or permeationcharacteristics for the chemicals of interest. The opening area mayinclude a single hole or a plurality of holes. Uptake rates aretypically measured in controlled chambers, where the concentration isknown, to calibrate the samplers for particular chemicals and samplingconditions.

High uptake rates generally provide greater sensitivity (i.e., allowlower concentrations to be quantified with shorter exposure duration),which can be an advantage in some instances. Lower uptake rates reducethe risk of the “starvation effect”, which occurs when the rate-limitingstep is transport of chemicals to the sampler instead of the uptake rateof the sampler itself. This situation results in a reduction in vaporconcentrations near the sampler, and a negative bias in the calculatedpassive sampler concentrations compared to the conditions under whichthe passive sampler was calibrated. Advection from wind and ventilationduring indoor and outdoor air sampling is often sufficient to minimizethe starvation effect. For soil gas sampling, advection is likely to beminimal and the rate of contaminant vapor replenishment in thegas-filled void space surrounding the sampler is likely to be limited todiffusive transport only, which is the focus of the mathematical modelspresented here. The uptake rate of the sampler can be increased ordecreased by design (such as by area and thickness of the membrane, forexample) to minimize the starvation effect and provide acceptablesensitivity.

Model for Quantitative Passive Soil Vapor Sampling

Passive soil vapor sampling is usually performed by drilling a hole inthe ground, removing soil, placing a passive sampler in the void spacecreated by drilling, sealing the hole from the atmosphere for theduration of the exposure, then retrieving the sampler and backfilling orgrouting the hole. A simple conceptual model of this scenario is asfollows:

-   -   Immediately after the hole is drilled and the soil is removed,        the void space fills with air. Assuming atmospheric air can        enter the void space with less resistance than gas flowing        through the surrounding soil, the initial concentration of        vapors inside the void space would be expected to be much lower        than that in the surrounding soil, and at worst could be assumed        to be essentially zero (i.e., atmospheric air is nearly        contaminant-free).    -   In most cases, passive samplers are emplaced and the space above        them is sealed without purging to attempt to remove atmospheric        air from the void space around the sampler. In conventional        passive soil vapor sampling methods, the seal has typically been        placed at the ground surface, so the void-space is exposed to        soil over the entire depth of the drillhole or borehole. This        invention includes a method for setting a seal at a depth just        above the sampler to provide better vertical resolution of vapor        concentrations. Purging may not be required if the sampling        duration is long compared to the time required for vapor        concentrations in the void-space to equilibrate with the        surrounding soil (which is the focus of the transient model).        Purging can be added as a step after passive sampler deployment        if, for example, the sampling period is short compared to the        equilibration time.    -   During the period of passive sampling, vapors diffuse into the        void space from the surrounding soil. If the void space is long        relative to its diameter and short enough that the geologic        properties and vapor concentrations are relatively uniform over        the vertical interval of the void space, then the diffusion will        be essentially radially symmetric (this has been assumed for        both the transient and steady-state models).    -   The rate of diffusive mass transport into the void space over        time will depend on the concentration gradient and effective        diffusion coefficient, and will gradually diminish as the        concentration in the void space increases (i.e., the        concentration gradient decreases, which is the driving force for        diffusion). The concentration in the void space will eventually        stabilize at a concentration slightly below the concentration in        the surrounding soil as long as some mass is being removed by a        passive sampler.    -   If the uptake rate of the sampler is small relative to the rate        of diffusion into the void space (a goal if the starvation        effect is to be small), then the steady-state concentration in        the void space will be similar to the concentration in the        surrounding soil, which is important for accuracy of the        concentrations measured via passive sampling.

Mathematical Modeling of Quantitative Passive Sampling

Passive soil vapor sampling involves: a) transport of vapors through thesoil surrounding the drill-hole into the void space in which the sampleris deployed; b) diffusion through the air inside the void space, and; c)uptake by the sampler. The free-air diffusion coefficient through theair inside the void space will generally be much higher than theeffective diffusion coefficient in the surrounding soil, so vaportransport through the air inside the void space is not expected to bethe rate-limiting step. This allows the mathematical analysis to focuson two components: The rate of vapor diffusion into the void space (the“diffusive delivery rate”, or DDR) and the rate of vapor uptake by thepassive sampler (“passive sampler uptake rate” or UR). Understanding therate of diffusion of vapors into the void space is necessary to designan appropriate uptake rate for the passive sampler, which both minimizesthe starvation effect and provides adequate sensitivity (ability to meettarget reporting limits with acceptable sample durations).

Influence of Soil Moisture on the Effective Diffusion Coefficient inSoil

The effective diffusion coefficient depends on the total porosity andwater-filled porosity. Understanding this relationship is helpful forcontext in the theory of passive soil gas sampling if diffusion is themain process delivering vapors to the void space in which the sampler isdeployed. P. C. Johnson and R. A. Ettinger have used equation (2) tocalculate the effective diffusion coefficient for subsurface gaseous andaqueous phase diffusion.

$\begin{matrix}{D_{eff} = {\frac{D_{air}\theta_{n}^{10/2}}{\theta_{T}^{2}} + \frac{D_{w}\theta_{w}^{10/3}}{\theta_{T}^{2}}}} & (2)\end{matrix}$

Where

D_(eff) is the effective diffusion coefficient [cm²/s]

D_(a) is the free-air diffusion coefficient [cm²/s]

θ_(a) is the air-filled porosity (volume of air/total volume of soil:dimensionless),

D_(w) is the aqueous diffusion coefficient [cm²/s],

θ_(w) is the water-filled porosity (volume of water/total volume ofsoil: dimensionless),

θ_(T) is the total porosity (θa+θw), and

H is the Henry's Law Constant (concentration in gas/concentration inwater).

Equation 2 was used to calculate D_(eff) for both transient andsteady-state models. Parameter values used for all calculations wereselected to be representative of trichloroethene (TCE, a common VOC) andare presented in Table 1.

TABLE 1 Parameter Values used in Model Simulations (representative forTCE) Parameter name Symbol Units Value Free air diffusion coefficientD_(air) cm²/s 0.069 Aqueous diffusion coefficient D_(w) cm²/s 0.00001Henry's Law Constant H dimensionless 0.40 (15° C.) Total porosity θ_(T)Volume of 0.375 voids/total Water-filled porosity θ_(w) Volume ofVarious water/total values from volume of soil 0.01 to 0.36

A series of calculations were performed using Equation (2) and theparameter values in Table 1 to show the relationship between theeffective diffusion coefficient and the water-filled porosity. Thecalculated D_(eff) values span a range from about 0.01 to about 0.00001cm²/s over a range of water-filled porosities from 1% to 36% in a soilwith 37.5% porosity as shown in FIG. 1. These values are indeed muchlower than the free-air diffusion coefficient (0.069 cm²/s), whichsupports the assumption that diffusion through the void space in whichthe sampler is deployed is not rate-limiting (which is consistent withthe assumption stated above). Other VOCs have similar diffusioncoefficients, so the general trends apply for most VOCs of interest forhuman health risk assessments.

FIG. 1 shows the difference between the effective diffusion coefficientof dry soils as compared to wet soils is a factor of more than 1,000.Passive samplers generally should be designed to accommodate the widestpractical range of soil moisture conditions to have broad applicability.

Two models (transient and steady-state) are presented to simulate thepassive sampling process.

Transient Model

The conceptualization for the transient mathematical model of radialdiffusion of vapors from soil into the void space is shown in FIG. 2.The mathematical model corresponding to FIG. 2 allows the diffusivedelivery rate of vapors from the soil to the void-space in which thesampler is deployed to be calculated for different soil water-filledporosity values, borehole diameters and chemical properties. FIGS. 2-6refer to the transient model.

Transient Model Simulations

A series of simulations were performed using the transient model to showthe relationship between the mass entering the void space from thesurrounding soil and time. These simulations initially do not accountfor mass removed by a passive sampler in the borehole, which would drawa small but finite amount of mass from the surrounding soil over time.The effect of adding a sampler is considered later.

Equation (1) can be re-arranged to express the diffusive delivery rate(DDR) to the void space as a function of the initial concentration ofvapor in the soil (C_(s) ⁰) and the mass of vapors entering the voidspace from the surrounding soil (M_(v)) during the deployment time (t),i.e.:

$\begin{matrix}{{DDR} = \frac{M}{C_{s}^{0}t}} & (3)\end{matrix}$

Equation 3 provides a basis for calculating a DDR value that can becompared to the sampler uptake rate directly, which is useful foridentifying the threshold uptake rate needed to minimize the starvationeffect. The mass entering the void space as a function of time is shownin FIG. 3 for a 2.54 cm (1-inch) diameter drill-hole, a C_(s) ⁰ of 100μg/m³ and a vertical interval of 10 cm, including simulations for avariety of different water-filled porosities (θ_(e)) and thecorresponding effective diffusion coefficients (D_(eff)) from FIG. 1.For all water contents simulated, the mass eventually reaches a steadyvalue as the concentration inside the void space equilibrates with thesurrounding soil. This is only representative of a borehole with nopassive sampler; however, the simulation is nevertheless instructivebecause it provides information on the time required for the void spaceto equilibrate with the surrounding soil as a function of the moisturecontent. For relatively dry soils (e.g., θ_(w)<0.1), the void spaceconcentration would be within 10% of the soil vapor concentration in aslittle as about 10 minutes. For very wet soils (e.g., θ_(w)=0.30), asimilar level of equilibration may require up to about one day. FIG. 3shows that the void-space equilibrates quickly with the surrounding soilvapor concentrations (within about an hour or less for all but very wetsoils).

The simulation results shown in FIG. 3 can also be used to calculate thecorresponding diffusive delivery rates of vapors from soil into the voidspace via Equation (3), as shown in FIG. 4. FIG. 4 shows the diffusivedelivery rate is in the range of about 0.1 to 10 mL/min during theperiod over which the void-space equilibrates with the surrounding soilvapor concentrations (about 0.1 day or less for all but very wet soil asper FIG. 3). The diffusive delivery rate decreases as the vaporconcentration in the void space approaches equilibrium with thesurrounding soil because the concentration gradient (which is thedriving force for diffusion) diminishes. For an equilibration time of 10minutes or less (corresponding to the equilibration time for dry soil),the diffusive delivery rate from the soil to the void space calculatedusing Equation (3) is about 5 mL/min. For an equilibration time of aboutone day (corresponding to the equilibration time for a very wet soil),the diffusive delivery rate is about 0.03 mL/min. Note that thesesimulations assume there is no passive sampler in the void space. Addinga sampler would remove a certain amount of VOC mass, which would sustaina higher concentration gradient and the average diffusive delivery ratewould be higher than simulated by this model, especially for longer-termdeployment intervals. Nevertheless, this provides an initial frameworkfor designing a preferred uptake rate for a passive sampler forquantitative soil vapor concentration measurement.

In absence of a passive sampler inside the void space, the diffusivedelivery rate (DDR) gradually slows down as the concentration inside thevoid approaches the concentration in the surrounding soil and theconcentration gradient diminishes. The relationship between the averageDDR and the percentage of the total mass transferred from the soil tothe void space is shown in FIG. 5. FIG. 5 shows that the diffusivedelivery rate is above 1 mL/min, except for very wet soils and when thevapor concentration in void-space is very close to the concentration inthe surrounding soil (i.e., when the concentration gradient driving thediffusion has diminished to a very low level).

For very dry soils, the average DDR is greater than 10 mL/min untilabout 90% of the mass has entered the void space. In this scenario, apassive sampler with an uptake rate of 10 mL/min may still provide datawith an acceptably small starvation effect (i.e., the sampler uptakerate remains below the diffusive delivery rate from the soil until themass delivered to the void space is about 90% of the steady-state value,so a negative bias of only 10% or less may be possible. For very wetsoils (θ_(w)=0.30), the average DDR is about 0.01 mL/min by the time thevoid space has nearly equilibrated with the surrounding soil (roughly 1day). However, for moisture contents typical of most vadose zone soils,an uptake rate of about 1 mL/min would be expected to result in anacceptably small starvation effect (i.e., for a water-filled porosity ofup to 25% in a soil with 37.5% porosity, a sampler with an uptake rateof 1 mL/min would be expected to result in less than 20% negative biasvia the starvation effect).

Superposition of Diffusive Delivery Rate and Uptake Rate

The transient mathematical model presented in the previous section isonly part of the process, and the uptake rate by the sampler is alsoimportant to consider. A transient mathematical model including2-dimensional radial diffusion to the void space (diffusive delivery),3-dimensional diffusion through the void-space to the passive samplerand uptake by the sampler is challenging to simulate mathematically.However, an approximate model can be derived by adding the diffusivedelivery rate (FIG. 4) and the sampler uptake rate to estimate theeffect of both processes occurring at the same time. This is anapproximation; however, as long as the uptake rate of the sampler islower than the diffusive delivery rate to the void space, the combinedmodel will only be different than the analytical model of radialdiffusion after the diffusion into the void space has very nearlyattained steady-state, at which time the diffusive delivery rate ofvapors into the void space will stabilize at the same value as theuptake rate of the sampler. FIG. 6 shows an example of the diffusiveuptake rate that would be expected if a passive sampler with an uptakerate of 1 mL/min was placed in the void-space simulated in FIG. 5.Within about one day, the delivery rate for all water-filled porositiesapproaches the uptake rate of the sampler. More specifically, FIG. 6shows that a steady-state condition would be achieved in a day or lessfor all water contents and this condition would be approached (within afactor of two) within an hour or less.

It should be noted that for very wet soils (water-filled porositygreater than 0.25), the steady-state delivery rate may be less than 1mL/min, in which case there are two possibilities: 1) a lower uptakerate sampler could be used, or 2) a negative bias attributable tostarvation may still be experienced. If the negative bias is predictableor acceptably small, the data may still be useful and this may bereasonably evaluated using the models presented here as long as theporosity and moisture content are known or can be reasonably estimated.

Steady-State Model

If the duration of passive sampling is long compared to the timerequired for the vapor concentrations in the void space to approachequilibrium with the surrounding soils, then a steady-state model wouldalso provide insight into the passive sampling mechanisms. For thiscase, the conceptual model is as follows:

-   -   The vapor concentration in the soil surrounding the void space        is uniform at C_(sg) beyond a radial distance of r₃ (some        distance beyond the radius of the borehole, where soil vapor        concentrations are unaffected by the borehole or passive        sampler),    -   Diffusion occurs in the region between the outer wall of the        drill-hole (radius=r₂) and r₃, through a cylinder of height, h,    -   The concentration inside the void space of the borehole (C_(bh))        is lower than C_(sg) by a factor δ=C_(bh)/C_(sg),    -   Radial diffusion occurs from the soil to the void space at a        diffusion delivery rate equal to the passive sampler uptake rate        for the majority of the sample deployment period.

The rate of mass transfer of vapors into the borehole via vapordiffusion through the surrounding soil (M1) is given by H. S. Carslawand H. C. Jaeger (1959);

$\begin{matrix}{{M\; 1} = \frac{2\pi \; {{hD}_{eff}\left( {C_{sg} - C_{bh}} \right)}}{\ln \left( \frac{r_{3}}{r_{2}} \right)}} & (4)\end{matrix}$

The rate of mass uptake by sampler (M2) is given by:

M2=C _(bh) ×UR  (5)

Setting M1=M2 gives:

$\begin{matrix}{{{UR}\left\lbrack \frac{mL}{\min} \right\rbrack} = {\frac{2\pi \; {h\lbrack{cm}\rbrack}{D_{eff}\left\lbrack \frac{{cm}^{2}}{z} \right\rbrack}\left( {1 - \delta} \right)}{{\ln \left( \frac{r_{3}}{r_{2}} \right)}\delta} \times {60\mspace{11mu}\left\lbrack {s\text{/}\min} \right\rbrack}}} & (6)\end{matrix}$

If a passive sampler is deployed in a nominal 1-inch diameter borehole(r₂=1.25 cm) and sealed within a 10 cm void space (h=10 cm), the uptakerates as a function of water-filled porosity calculated using equation 6are shown in FIG. 7. FIG. 7 depicts the diffusive delivery ratecalculated using the steady-state model corresponding δ values of 0.5,0.75 and 0.95 as a function of water-filled porosity for a 10 cm talland 2.5 cm diameter void-space assuming r₃=1 m, where δ is the ratio ofthe vapor concentration in the void-space divided by the vaporconcentration in the surrounding soil and r₃ is the radius beyond whichthe soil vapor concentrations are unaffected by the borehole or sampler.FIG. 7 shows that an uptake rate of 10 mL/min might be acceptable forvery dry soil if the data quality objective was to quantifyconcentrations within a factor of two (i.e., δ=0.5), however; an uptakerate of 1 mL/min would be more suitable for soils with up to 40% watersaturation (water-filled porosity of 15% in a soil with total porosityof 37.5%), assuming a more stringent data quality objective of +/−25%(i.e., δ=0.75). Progressively lower uptake rates would be required tofurther reduce the negative bias or meet typical data quality objectivesin very wet soils. For example, a sampler with an uptake rate of 0.1mL/min would only cause a 50% reduction in the vapor concentrations inthe void-space for soils with a water-filled porosity of up to 30%.FIGS. 7 and 8 relate to the steady-state model.

A sensitivity analysis on the r₃ value is shown in FIG. 8 for the sameconditions as in FIG. 7 and a δ value of 0.75. FIG. 8 shows thecalculated uptake rate corresponding to various r₃ values (r₃ is thedistance beyond which soil vapor concentrations are unaffected by theborehole and passive sampler) as a function of water-filled porosity fora 1-inch diameter drill-hole assuming δ=0.75. FIG. 8 shows that themodel results are relatively insensitive to the value selected for r₃.

Sensitivity Considerations

There is a practical lower limit to the uptake rate for passive samplingimposed by the exposure duration (or sampling time period) needed toachieve a specified concentration reporting limit. Equation (1) can berearranged to calculate the exposure duration (t) required to achieve atarget reporting limit (C_(o)) if the uptake rate (UR), and thelaboratory mass reporting limit (M_(RL)) are known:

$\begin{matrix}{t = \frac{M_{RL}}{C_{o}{xUR}}} & (7)\end{matrix}$

For example, consider an initial soil vapor concentration of 100 μg/m³of TCE and a sampler with an uptake rate of 1 mL/minute. A detectablemass of TCE (approximately 0.05 μg via solvent extraction, GC/MS) wouldbe sorbed by the sampler in less than a day. This demonstrates that alow-uptake rate sampler can provide practical sensitivity within areasonable amount of time and still avoid or minimize the starvationeffect. However, if the uptake rate was reduced to 0.1 or 0.01 mL/min,the exposure duration would need to increase proportionately, and thereare logistical challenges with exposure durations of 10 to 100 days(costs of return travel to field sites, security over longerdeployments, etc.). The minimum detectable mass can be reduced if neededusing thermal desorption instead of solvent extraction as the laboratorysample preparation method, so the invention allows for both options.Thermal desorption allows the minimal detectable mass to be much lower(about 0.001 μg), which would provide the same sensitivity(concentration reporting limit) with the same sampling time for anuptake rate of 50 times lower than a sampler using solvent extraction.

Summary of Mathematical Model Simulations

In order for a kinetic passive sampler to provide quantitative soilvapor concentration data, it must have a known and reliable uptake ratefor all of the compounds of interest. In order to minimize thestarvation effect, the passive sampler uptake rate should be lower thanthe rate of diffusive delivery of vapors into the void space from thesurrounding soil. In order to provide good sensitivity (ability todetect low concentrations) without an excessive sampling period, it isalso important that the sampler uptake rate not be unnecessarily low. Anuptake rate in the range of about 0.1 to 10 mL/min may be suitable,depending on the soil moisture content, and uptake rates in the range ofabout 0.1 to 1 mL/min are likely to be suitable over a practicably widerange of moisture contents typically found in unsaturated soils.

Sampling Device

FIGS. 9, 10 show samplers according to illustrative embodiments of theinvention. FIG. 9 depicts a disposable sampler and FIG. 10 depicts areusable sampler. The sampler comprises a container 26 (for example,approximately 0.8 mL glass vial, or equivalent) filled with a sorbentmedium (e.g. Anasorb 747, or one or more of several other suitablemedia), and the opening of the container is covered with a thin filmmembrane 27 with a uniform thickness, for example polydimethylsiloxane(PDMS). In this embodiment, membrane 27 is used to seal the container(for example, using an aluminum crimp cap 28). The reusable sampleremploys a screw cap 29, preferably of plastic, at the bottom ofcontainer 26, to facilitate cleaning so it can be reused. The device isdesigned to optimize the uptake rate to within a range of valuescalculated mathematically to minimize or eliminate the starvation effectfor most soil types and provide acceptable sensitivity with a practicalsample period. The membrane thickness can be adjusted to manipulate theuptake rate depending on the requirements. For example, thicknesses fromabout 25 μm to about 150 μm may be used. Additionally, or instead, thevial dimensions, in particular the area of the vial opening, may bevaried, as the opening itself affects the uptake rate. The opening areamay include a single hole or a plurality of holes. As an example, vialsof 1.8 mL and 0.8 mL may be used, which will vary in opening size. For aspecific vial size, PTFE washer pairs can be incorporated to furtherdefine the area exposed to the sample.

The passive sampler may be fabricated, according to an illustrativeembodiment of the invention, by cutting a membrane to fit the opening ofthe container (vial); adding sorbent to the container, assembling themembrane and cap and crimping to seal. A support may then be attached towhat is the bottom portion of the sampler when filling. The sampler isthen turned upside down for lowering into a void space for sampling,such that the sorbent remains in contact with the inner surface of themembrane throughout the sampling period. Alternatively, the amount ofsorbent with respect to the size of the vial can be selected to achievethe desired membrane contact. Keeping the sorbent in contact with theinner surface of the membrane during the sampling period preferablymaintains a zero-sink condition (vapor concentrations near zero) at theinner surface of the membrane and improves consistency of theconcentration gradient that drives the uptake of VOCs into the sampler.

During the exposure period, vapors dissolve into the membrane andpermeate across it at rates that are proportional to the lineartemperature programmed retention indices (LTPRI) of the compounds ofinterest in a gas chromatographic column coated with a stationary phaseof the same material as the membrane of the sampler (e.g., PDMS, orsimilar material).

The rate of permeation of a gas across a fluid membrane is 1)proportional to the difference in the concentration of the analyte onthe surface on either side of the membrane; 2) proportional to the crosssection of the membrane; and 3) inversely proportional to the thicknessof the membrane. The following equations apply:

-   -   Wherein:    -   M=Amount of analyte collected by the sorbent    -   D=Diffusion coefficient of the analytes in the membrane        (increases with temperature)    -   A=Area of membrane    -   C_(ms)=Concentration of the analyte “on” the membrane surface in        contact with the sorbent.    -   C_(ma)=Concentration of the analyte “on” the membrane surface        exposed to air or gas.    -   t=Sampling time    -   L_(m)=Membrane thickness    -   K=Partition coefficient of the analyte between air and the        membrane (decreases with temperature)    -   P=Permeability constant of the polymer towards the analyte        (P=D×K)    -   Co=Concentration of the analyte in air    -   k=Calibration Constant (time/volume)    -   k⁻¹=Uptake rate (volume/time) (the inverse of the calibration        constant)

The uptake rate may be varied by adjusting the area or thickness of themembrane. A combination of the two adjustments can also be made toachieve the desired uptake rate.

The linear temperature-programmed retention index (LTPRI) for VOCs in achromatographic column with a coating substantially similar to thematerial used to make the membrane of the sampler (e.g., PDMS)correlates to the calibration constant as follows:

The LTPRI—Calibration Constant correlation is useful when the identityof the pollutant is unknown at the time of sampling because it allowsthe uptake rate to be calculated with reasonable accuracy for thosecompounds for which the uptake rate has not been experimentally measuredin controlled laboratory chamber experiments. The correlation alsoprovides the possibility of estimating total petroleum hydrocarbons,which is not possible with other diffusive samplers.

The membrane is hydrophobic (for PDMS, the uptake rate for water isabout 60 times lower than the uptake rate for toluene), which reducesthe risk of analytical interferences attributable to excessive moisture.Existing tube samplers do not inhibit the entry of water vapor, andtherefore, are subject to potential interferences attributable to water.

Various extraction schemes may be used to process/analyze the samplecollected with the passive sampler. In a first illustrative embodimentof the invention, the cap is de-crimped and desorption solvent (forexample, carbon disulfide, hexane, etc.) is added to the vial. The vialcan then be closed by crimping with an aluminum crimp cap with a Teflon®lined septum. The vial is then shaken. A sub-sample of the desorptionsolvent can then be introduced directly into a gas chromatograph (GC).In another embodiment, the vial cap is de-crimped and the contentstransferred to a 4 mL or other size screw cap vial. Desorption solventis then added, the vial is capped and the vial is shaken. The extractedsolvent is transferred to a 2 mL or other suitable size vial, which issealed by crimping with an aluminum crimp cap with a Teflon® linedseptum. The sample can then be introduced into a GC auto-sampler. If athermally-desorbable sorbent is used (e.g., Tenax TA, Carbopack B,Carboxen 1016 or similar), the sorbent can be transferred from theWMS-LU sampler to an Automated Thermal Desorption (ATD) tube prior toanalysis. The mass of each compound is determined using routine gaschromatography with mass spectroscopy or similar laboratory analysismethods.

Illustrative sampling methods for using the passive sampler to measureconcentrations of volatile organic compounds in soil gas will now bediscussed.

Sampler Activation and Deployment

The sampler is activated (i.e., begins to sorb chemicals from itssurrounding) as soon as it is removed from the polycoated aluminum pouchin which it may be stored and the 20 mL glass overpack vial which may beused to protect the sampler from exposure to chemicals during shipment.It is preferable to minimize the above-ground exposure time to avoidpotential interferences from background sources of volatile organiccompounds when the objective is to measure subsurface vaporconcentrations.

During the deployment period, the sampler should be positioned such thatthe sorbent inside the vial is in direct contact with the membrane.

Sampler Retrieval

The sampler is deactivated by returning it (including the plasticholder, if used) into the 20 mL glass overpack vial, or other suitableprotective packaging. The overpack vial can be sealed, for example byscrewing the cap tightly onto the overpack vial and putting Teflon® tapearound the outside of the cap/vial junction. The sampler is nowdeactivated.

Illustrative methods involve exposing the sampler to a void space in thesubsurface through a hole drilled to a specified target depth.

The sampler is lowered into the borehole and the sampler is eitherwrapped with aluminum insect mesh or a coil of stainless steel wire, orother component of suitable material, to protect the membrane fromcontacting soil surfaces during deployment and retrieval.

The borehole should be sealed after deployment of the sampler to preventatmospheric air leakage into the borehole or losses of VOC to theatmosphere during the sampling period. Sampling can be accomplished in avariety of ways, including the three ways, described below:

1) Deployment in a semi-permanent passive soil vapor monitoring probe:If the geologic materials are not cohesive and there is a risk theborehole will collapse, or if periodic monitoring is planned usingreproducible sampling conditions, or if the depth of deployment isgreater than about 3 m, it may be preferable to install a semi-permanentpassive soil vapor monitoring probe.

Two features are preferred for the passive soil gas probe: 1) a rigid,inert pipe should be suspended above the bottom of the borehole, so thelowest part of the borehole allows open communication between thesurrounding soil and the open void space in which the sampler will bedeployed, and 2) the annulus between the pipe and the borehole wall mustbe sealed in such a way as to prevent air flow and prevent the seal fromfilling the void space at the bottom of the pipe. The diameter of thepipe must be large enough to accommodate the sampler (e.g., about 1 or 2inch).

FIGS. 11 and 12 are schematic diagrams of two options for semi-permanentprobes for passive soil vapor sampling according to an illustrativeembodiment of the invention. In FIG. 11, a passive sampler 2 extendingfrom a nylon line 3 is deployed in a borehole 4 having walls 5. A 2-in(or other suitable size) inert pipe 6 is disposed within borehole 4, andis supported by stilts 7. The pipe may be made of any inert, rigidmaterial (for example, of PVC). A gasket 8 surrounds pipe 6 toward thepipe's lower end, which in this example is approximately 2 feet from theborehole bottom 10 and approximately 10 feet below ground surface 11(these dimensions can be varied as appropriate for a specific verticaldiscretization of soil vapor concentration monitoring). Space betweenborehole wall 5 and pipe 6 is filled with a material such as bentoniteslurry to form an annular seal 9. A slip cap 12 closes the space inwhich passive sampler 2 is deployed. Alternatively, a deeper seal couldbe placed using the same method for temporary holes that is describedbelow. The void space is designated by reference number 13.

FIG. 12 is a similar schematic diagram of a semi-permanent probe forpassive soil vapor sampling according to an illustrative embodiment ofthe invention, with a slightly different option for the annular seal andtwo holes through a slip-cap 38 having a purge line 39 for purging andcollection of active samples within borehole 16, if needed or desired. Apassive sampler 14 extending from a nylon line 15 is deployed in a 4-in(or other suitable size) auger hole 16. A 2-in (or other suitable size)PVC pipe 17 is supported by stilts 18. A stainless steel ring clamp 19is positioned at the lower end of pipe 17 to fasten the plastic sleeve21 and stilts 18 to the pipe, in this example at about 6-18 inches (orother dimensions as needed to suit site-specific conditions andobjectives) above the borehole bottom 20. A plastic sleeve 21 with adiameter larger than the borehole wall is disposed within borehole 16and surrounding the pipe 17. Within pipe 17 is a ⅛-in stainless steeldrop tube 22. Pipe 17 extends to approximately 3 ft from ground surface25 in this example, but this can be varied a needed. Compacted sand 23fills the space between the plastic sleeve 21 and the outside surface ofpipe 17 to form a seal between the pipe and the borehole wall. Passivesampler 14 is shown extended to void space 24.

2) Deployment in an open hole: If the geologic materials are cohesiveenough to stand open, and the sampling depth is about 3 m or less, anopen hole may be used for deployment. After placement of the sampler,the hole may be sealed a short distance above the sampler using aflexible and relatively inert plastic sleeve (e.g., polyethylene orethyl vinyl alcohol) of a diameter slightly larger than the boreholewith a plug inside the plastic sleeve of foam rubber or similarcompressible material to press the sleeve against the wall of theborehole with sufficient force to form a seal, but with a pressure smallenough that the seal can easily be removed by pulling up on the sleeveat the end of the sampling period. This kind of seal could also be usedin a semi-permanent probe, if desired. According to an illustrativeembodiment of the invention, such a seal may be placed as shown in FIGS.13a-c by taking the following steps: a) Cut the plastic sleeve 36 to alength of about 30 cm longer than the depth from ground surface 30 towhich the seal is desired. Close the bottom of the sleeve, for example,by folding and stapling the bottom closed or by heat-sealing, asdesired;

b) Compress a foam plug 31 and place it inside one end of a thin-walledrigid pipe (plastic or metal) slightly smaller in diameter than adrilled hole 32. Place a dowel 33 of smaller diameter than the pipeinside the pipe, and place the pipe inside the plastic sleeve;

c) Drill the borehole 32 and remove soil. Promptly lower a sampler 34 tothe target depth, and secure the retrieval tether (nylon line orstainless steel wire for example) 35 at ground surface 30;

d) Lower the plastic sleeve, pipe and dowel to a depth slightly abovethe passive sampler 34 as shown in FIG. 13 b.

e) Hold the dowel stationary and lift on the pipe until the dowelextends below the bottom of the pipe, which will force the foam out ofthe pipe and allow it to expand, pressing the sleeve against borehole 32wall and forming a seal 36 just above the passive sampler as shown inFIG. 11 c.

f) Seal 36 remains in place for the duration of the sample deployment,at which point the plastic sleeve is retrieved from borehole 32.

g) Retrieve passive sampler 34 after seal 36 is removed. Plug theborehole, such as with a cement/bentonite grout or according to localregulations.

The plastic sleeve is preferably made of an inert and flexible material.Examples of materials include, but are not limited to, high densitypolyethylene, ethyl vinyl alcohol, or fluoropolymers such as Teflon®. Acombination of aluminum foil with other materials could also be used toform a more inert seal, if needed (e.g., if the target chemicals arestrongly sorbed by plastics).

The method shown in FIGS. 13a-c can be used in either a temporaryborehole with no casing or in a semi-permanent probe with casing

3) Sub-Slab Sampling: For sampling below concrete floor slabs thesampling protocol is, for example:

a) Prepare the sampler to protect the membrane from contact with thesoil;b) Drill a hole through the floor;c) Lower the sampler into the hole through the floor;d) Seal the hole with an inert, removable stopper for the duration ofthe sampling period;e) At the end of the sampling period, remove the stopper and the samplerfrom the hole, andf) seal the hole with grout or other suitable sealant.

FIGS. 14a,b show relative concentration (passive/active, or C/Co) at afield sampling demonstration site using soil gas probes as shown in FIG.11 for 1,1-dichloroethene (1,1-DCE) (FIG. 14a ) and TCE (FIG. 14b ),respectively. FIGS. 14a,b show that a sampler according to anillustrative embodiment of the invention (the WMS sampler) yieldsrelative concentrations (C/Co, where C is the passive samplerconcentration and Co is the concentration measured via conventionalactive sampling) very near the ideal value of 1.0 for both TCE and1,1-DCE with no notable dependence on the sample duration (from 1 to11.7 days). Other samplers were included in this experiment (and arealso shown of FIGS. 14a,b ), which showed either a low bias attributableto the starvation effect, poor retention in longer-term samples, or lessconsistency than the WMS sampler. FIG. 15a shows the correlation betweenpassive samples and Summa® Canister Samples using probes as shown inFIG. 12, and FIG. 15b shows the correlation between passive samplers andSumma® canister samples using sub-slab probes. Both FIGS. 15a,b includelinear regressions and correlation coefficients (R²). FIGS. 15a,b showthat the WMS sampler has a better correlation to conventional activesoil vapor samples (via Summa canisters) than other samplers tested forsoil gas and sub-slab samples over a concentration range of about 100μg/m³ to over 10,000 μg/m³.

FIG. 16 shows the relative concentration (passive/Summa®) for theWMS/low-uptake sampler in a 1-inch (2.54 cm) diameter open borehole(such as in FIGS. 13a-c ) open from 4 to 5 feet below ground surface ata field sampling demonstration site. FIG. 16 shows that the WMS-LUsampler provides reasonably accurate and precise concentrations fortetrachloroethene (PCE), TCE, cis-1,2-dichloroethene (cDCE) andtrans-1,2-dichloroethene (tDCE) over durations ranging from 1.7 hours to18.9 hours.

FIGS. 17a,b show relative concentration (C_(passive)/C_(active)) versusuptake rate (UR) (FIG. 17a ), and (UR×sampling time)/Void Volume (FIG.17b ) for data from controlled field experiments with several differentpassive sampler types. FIGS. 17a,b show that negative bias from thestarvation effect is minimized when the uptake rate is about 1 mL/min orless or when the product of the uptake rate and the sample duration isless than the volume of the void space for probes that are purged at theoutset of the sampling period.

Deployment Time

The passive sampler deployment time can be calculated using either thetarget reporting limit (in areas of low vapor concentrations) or theexpected vapor concentration if it is known from previous monitoringevents or can be reasonably estimated from the field screening readings.The minimum deployment time can be calculated using the followingequation:

${{Deployment}\mspace{14mu} {time}\mspace{14mu} ({minutes})} = \frac{{Analytical}\mspace{14mu} {Limit}\mspace{14mu} {of}\mspace{14mu} {{Quantitation}{\mspace{11mu} \;}({ng})} \times 1,000}{\begin{matrix}{{Expected}\mspace{14mu} {Concentration}\mspace{14mu} \left( {{µg}\text{/}m^{3}} \right) \times} \\{{uptake}\mspace{14mu} {rate}\mspace{14mu} \left( {{mL}\text{/}\min} \right)}\end{matrix}}$

If the concentration is not known, or if it is below the limit ofdetection of the field screening instruments, then the estimatedconcentration in the equation above can be replaced with a value equalto or less than the risk-based target concentration.

In an exemplary embodiment of the invention, the sampler is smaller (0.8mL vial) than a prior design of polydimethylsiloxane membrane sampler,which was a 1.8 mL vial. The smaller size vial has a smaller opening,and this reduces the uptake rate to within the optimal range of about0.1 to 1 milliliter per minute (mL/min). The smaller size (with all elseequal) would have a minimum detectable vapor concentration about 5 timeshigher than the larger size for the same exposure duration. Soil gasrisk-based screening levels are not as low as screening levels forindoor air samples, so for the purpose of soil vapor sampling, the lowuptake rate is typically not a significant limitation, and adequatesensitivity can still be generally achieved with an exposure duration ofone day or less. The sensitivity can also be improved using thermaldesorption instead of solvent extraction as the method of samplepreparation, which reduces the lowest measurable mass (M) from about 50nanograms to about 1 nanogram or less. The membrane thickness can beincreased to decrease the uptake rate as well, in which case, the 1.8 mLvial size may be used for a low-uptake rate sampler, if and as desired.Other illustrative vial sizes and ranges include: less than 1.8 mL, lessthan 5.0 mL and approximately 0.8 mL to 2.0 mL. As noted previously, thevial size and hence the membrane area may be selected along with themembrane thickness to achieve the desired uptake rate.

A number of variables will determine the optimum uptake rate. Forexample, if the soil is dry, the uptake rate can be a little higher andif it is wet, it needs to be lower. So, sampler uptake rates in therange of about 0.01 to about 10 mL/min, for example, can potentiallyresult in relatively unbiased quantitative passive soil vapor sampling,depending on the soil moisture. The soil moisture will not always beknown in advance, so a lower uptake rate is generally better (applicablein a wider range of conditions). As noted above, a lower uptake ratetypically means the sample will need to be left in the ground longer toget enough analyte mass inside to be detected by the laboratory. If asampler with an uptake rate of 1 mL/min needs 24 hours, then one with anuptake rate of 0.1 mL/min needs 10 days. Therefore, the sampling timeneeded to achieve a desired minimum detectable concentration may be alimiting factor. Additionally, each compound has a slightly differentuptake rate, so this factor must be considered. Accordingly, 0.1 to 1mL/min is a “sweet-spot”, and will usually be the preferred range, butthis is approximate and can differ depending on site-specific variablesand objectives. The preferred uptake rate for a particular soil porosityand moisture, particular chemical or suite of chemicals, particularlaboratory sample preparation method (solvent extraction or thermaldesorption) can be determined using the mathematical methods describedherein.

The sampler can be used with sorbents that are designed to perform bestwith thermal desorption or solvent extraction methods of samplepreparation. It can also be made with clear or amber glass vials,plastic or metal containers. The membrane area and thickness can bemodified to optimize the uptake rate for specific soils or chemicals.And finally, the exposure time can be adjusted to provide a desiredreporting limit.

The sampler can be equipped with additional features aimed at protectingit from direct contact with soil (e.g. a wire mesh wrapping, a cage-likeenclosure, etc.) and various types of tethers for retrieval from thesubsurface (stainless steel wire, nylon line, etc.).

The reliability, accuracy and precision of passive samplers in generaldepend on the consistency of the uptake rate. For the sampler, themembrane is preferably manufactured with very tight tolerances on thethickness of the membrane. Furthermore, the diameter of the opening ofthe vial directly affects the uptake rate. In an exemplary embodiment ofthe invention, the combination of the diameter and thickness of themembrane achieves a desired target uptake rate range of about 0.1 to 1mL/min.

Various embodiments of the invention have been described, each having adifferent combination of elements. The invention is not limited to thespecific embodiments disclosed, and may include different combinationsof the elements disclosed or omission of some elements and theequivalents of such structures, including those of any prior artembodiments of samplers or sampling methods.

While the invention has been described by illustrative embodiments,additional advantages and modifications will occur to those skilled inthe art. Therefore, the invention in its broader aspects is not limitedto specific details shown and described herein. Modifications, forexample, to the specific structure of the sampler and mathematicalmodels, may be made without departing from the spirit and scope of theinvention. Accordingly, it is intended that the invention not be limitedto the specific illustrative embodiments, but be interpreted within thefull spirit and scope of the appended claims and their equivalents.

Claimed is:
 1. A passive kinetic sampler for quantitative passive soilvapor concentration measurement comprising: a container filled with asorbent medium; wherein selected sampler dimensions constrain the uptakerate to match values that minimize or eliminate a starvation effect ascalculated via mathematical models; wherein the mathematical modelscalculate the diffusive delivery rate of vapors to a void space in whicha passive sampler is deployed and depend at least in part on soilmoisture and porosity; and wherein the uptake rate, as constrained bythe selected sampler dimensions, is less than or about the delivery rateof vapors from surrounding soil, so the concentration of vapors in thevoid space within which the sampler is exposed is similar to theconcentration in the surrounding soil gas throughout the majority of thesampling interval.
 2. The sampler of claim 1 wherein the container has avolume of approximately 0.8 to 2.0 mL.
 3. The sampler of claim 1 whereinthe sampler container is smaller than 1.8 mL.
 4. The sampler of claim 1wherein the sampler container is smaller than about 5.0 mL.
 5. Thesampler of claim 1 wherein the sorbent medium is suitable to retain andrecover the target analytes consisting of a method selected from solventextraction and thermal desorption.
 6. The sampler of claim 1 wherein theuptake rate is within the range of about 0.1 to 1 milliliter per minute(mL/min).
 7. The sampler of claim 1 wherein the uptake rate is withinthe range of about 0.01 to about 10 milliliter per minute (mL/min). 8.The sampler of claim 1 wherein the sampler dimensions include the areaof openings through which the sorbent material is exposed to the voidspace.
 9. The sampler of claim 8 wherein the area of openings optimizesthe uptake rate for a specific chemical(s).
 10. A method toquantitatively measure concentrations of volatile organic compound (VOC)vapors below the ground surface comprising: providing a passive sampleraccording to claim 1 that sorbs or traps VOC vapors at known uptakerates (UR), which allows the concentration (C) to be calculated from themass (M) of each compound sorbed and the exposure time (t) of the sampleusing the following equation: $C = \frac{M}{{UR} \times t}$
 11. Themethod of claim 10 wherein the mathematical models include asteady-state and transient mathematical model employing an effectivediffusion coefficient derived at least in part from the soil moistureand porosity.
 12. The method of claim 10 using either thermal desorptionor solvent extraction as a method of sample preparation and selectingsorbents depending on the sample preparation method used.
 13. The methodof claim 10 wherein the sampler dimensions include the area of openingsthrough which the sorbent material is exposed to the void space and themethod further comprises selecting the area to minimize or eliminate thestarvation effect.
 14. The sampler of claim 13 comprising selecting thearea of openings to optimize the uptake rate for a specific chemical(s).15. The method of claim 10 wherein sampling occurs primarily bydiffusion and permeation, as compared to forced advection.
 16. Themethod of claim 10 wherein the container has a volume of approximately0.8 to 2.0 mL.
 17. The method of claim 14 wherein the sampler containeris smaller than 1.8 mL.
 18. The method of claim 10 wherein the samplercontainer is smaller than 5.0 mL.
 19. The method of claim 10 wherein theuptake rate is within the range of about 0.1 to 1 milliliter per minute(mL/min).
 20. The method of claim 10 wherein the uptake rate is withinthe range of about 0.01 to about 10 milliliter per minute (mL/min). 21.A method of sampling to form a seal just above a passive sampler,including: providing a plastic sleeve; compressing a foam plug; placingthe compressed foam plug inside one end of a substantially rigid pipe;placing a dowel inside the pipe; placing the pipe inside the plasticsleeve; drilling a borehole and removing soil; providing a sampleraccording to claim 1; lowering the sampler to a target depth; loweringthe plastic sleeve, pipe and dowel to a depth slightly above the passivesampler; and lifting the pipe while holding the dowel substantiallystationary until the dowel extends below the bottom of the pipe, therebyforcing the foam out of the pipe and allowing it to expand, pressing thesleeve against borehole wall and forming a seal just above the passivesampler.